Looks like it's the API key. I'd created a wordpress.com user to use Jetpack, and it had a new API key.
I pulled my old API key from the DB.
When I forced Jetpack to use the old API key, it showed my old data.

Is there a "proper" way to either
(a) copy data from the old API key to the new one
(b) associate the site's old API key with a wordpress.com login so Jetpack will use its data
(c) tell Jetpack to use the site's API key rather than the user's API key?

Yes, I have. Multiple times. I must have not communicated that clearly before.

It's very nice of you to try to help me, but I would like to actually make some progress toward resolving my particular issue, instead.

My problem is that my current Stats data is associated with one API Key, but the WP.com account ("r2bizzy") that I set up for Jetpack has a different API Key.

I think I need to figure out which WP.com account is associated with the API key that has my stats. I am not sure how to do that, though I will try using my admin email.

If you understand what I am saying here, and have an idea of how to determine the account/email associated with my old API key, I would love to hear about it.
Alternately, if you are aware of a way to associate one API Key's stats with another OAuth login or API key, that would be lovely.

1. To help us link this public question to the private one you're creating, please reference this public question's URL: http://en.forums.wordpress.com/topic/how-do-i-migrate-wp-stats-to-jetpack
2. What you believe your old API Key was
3. What you believe your current API Key is
4. Reactivate/Reconnect Jetpack (again) and go to your Admin → Jetpack. At the bottom of the page, there should be a "Debug" link. Click the link and some debugging information should appear. Please paste that information in the contact form as well. Note that the debug information is also sensitive and should not be posted publicly.

When you submit the contact form, please be sure to select that the question is a private one.

Sorry for the hassle, as you can see, we don't have an easy way to move a conversation from a public question to a private one.

Yes :) We responded to the private support ticket you created (thanks!). You should have received an email from us with subject "Problem migrating WP Stats data to Jetpack (1048132)".

The email we sent asked for screenshots of the problem, since it's not clear to us what exactly is broken. Jetpack doesn't use those API keys at all, so we're not sure why editing them breaks/fixes the bug you're experiencing.